A self-similar solution to time-fractional Stefan problem

TL;DR

This paper introduces a fractional Stefan problem incorporating memory effects via a time-fractional derivative and derives a special self-similar solution to this modified model.

Contribution

It presents the first derivation of a fractional one-phase Stefan problem with a Riemann-Liouville derivative and provides an explicit self-similar solution.

Findings

Derived a fractional Stefan model with memory effects

Obtained a special self-similar solution

Extended classical Stefan problem to fractional calculus

Abstract

We derive the fractional version of one-phase one-dimensional Stefan model. We assume that the diffusive flux is given by the time-fractional Riemann-Liouville derivative, i.e. we impose the memory effect in the examined model. Furthermore, we find a special solution to this problem.